Beautiful places!
They are both somewhat accessible, depending where you are and what you want to visit. We have travelled both, exclusively with public transport. We did a sit in Newquay, and from there we were able to see everything on our list, such as Penzance, Port Isaac, Tintagel Castle, Padstow & Bude. We couldn’t get to the South of Cornwall with public transport though, as this was too far (to get from Newquay to Truro & Falmouth, for example). But for me, Port Isaac, Penzance & Newquay were the top of my list and I was really happy that we could see them all with the busses. There is a bus line called the Atlantic Coaster and another one called the tinnie (or something like that) which we used a lot, and they are large double decker ones, some with an open top roof which was really nice as we went through the narrow country lanes.
For Wales, we did a sit in Newport and could easily see Cardiff from there, and we did another 2 sits up north in Rossett & Oswestry, from which we could easily see Wrexham, Chester, Shrewsbury & Llangollen. We were lucky enough that one of my fiancé’s fishing buddies was able to take us on a car trip to Snowdonia, which was incredible and we wouldn’t have been able to get there with public transport. It really depends what area of Wales you want to see, but it’s too long to get from the south to the north of Wales with public transport for just a single day trip, so I’d suggest you pick an area and see the attractions nearby. Some places in Wales are quite remote, so just check what’s accessible via public transport first.
June weather for Cornwall was lovely - we had clear skies and warm weather every single day! Summer in Wales was very wet & windy - it bucketed down non stop the whole time, but we still made the most of it 
Hope that all helps!
